how to generate poisson with single argument mean?

In my algorithm i have to generate random number using poisson(lembda) where lembda is the single argument which is updated by code.now i know the equation of poisson and the value of lembda but i dont know which value of k should i take in equation of poisson to get the random number.can u explain with one example as initially my lembda =1.

F(k,λ ) = [(λ)^k * e^(-λ )] / k!

what value should i take as k in above equation so that it generates random number >= 1????

In the normal poisson pdf k is the number of events, while λ is mean.

In your random generator, you shouldn't be entering k, this should be returned by the generator.